Oo, I love the Teddy Roosevelt idea. You could do several historical world leader themed cards. A Japanese emperor type, a Ghengis Kahn type, a Sadam type, a Castro (his weapons are clearly cigars and communism) type, a British king. You could do King John and do a Magna Carta card, but that might be a little too esoteric.

I was thinking Teddy Roosevelt would make a fantastic character card. He carries a big stick/is a big game hunter, he gave a speech after being shot---without pause---and split the Republican vote in the 1912 election by creating his own party to defeat Taft.

For a battlefield I feel like a college dorm room would be a lot of fun---food everywhere, mountains of dirty laundry, the free spaces need to be hopped across like stones in a stream ect.

For an item, the US Constitution. Because, because. I'm not an American History nerd or anything ;)

Firstly, I feel it would make a really interesting artwork for a card, Secondly, this is a mythology that rarely gets looked at so it is not as over used as some others, Thirdly, even though most people might not be aware of the serpent, I'm sure they will be able to come up with a fantastic stories in any case.

I really like a lot of the suggestions here - I especially like the recent generic Goddess, Jack the Ripper, Utility Belt and Hive Mind suggestions. And I really hope you do a Monkey King card!

I've been thinking what I plan on doing with my blank cards and thought I'd share some of them here, though I thought of some of these specifically to reference other tabletop games, as I'll probably mostly be playing this at my uni's tabletop gaming society. Obviously for that reason not all are possible, just thought others might enjoy seeing them.
Warriors:
-Munchkin - (in reference to both the game and the trope) A dimunuitive warrior, he is callous and doesn't much care for backstory.
-Man with a Giant Head - (a lot of us enjoy playing Sopio at the tabletop gaming society, I thought some of its ideas would translate to Story War quite nicely) He's married, got two kids, has a pet giant cat and still has time to party. Basically, he's living the dream.
-Time-Travelling Tortoise - (another Sopio one) He's pretty darn slow, but always arrives with time to spare. (So that's how he beat the hare...)
-Dungeon Master - (This and the rest of the warriors are DnD inspired - I know you're trying to avoid those, but I think at least a few of these are well established enough to work well) He controls powerful magics that affect the battlefield and summon creatures to battle his foes. He can't affect free will though, and he's easily bribed with pizza.
-Assassin - This femme fatale knows her way around crossbows and swords as well as how to slip in and out of sight.
-Barbarian - She might not be the sharpest axe in the barbarian cache of weapons, but once she goes into a rage and starts charging, nothings going to stop her.
-Beast Master - This ranger focuses less on bows or swords and more in the command of nature. With his wolf companion by his side, they're an unstoppable duo.
Battlefields:
-Hexagon Island - (basically Catan) This newly discovered island has begun attracting settlers interested in the island's rich resources of wheat, sheep, wood, clay, stone and treachery.
-Chess Board - This checkered battlefield is strewn with the remains of a once great battle. Some warriors might find their movement here restricted...
Items:
-Sex-Changing Belt - (a fun little trope of some RPGs that I enjoy playing with) This stylish belt looks utterly harmless. It feels like a good idea to put it on...
-The Right to Bear Arms - (one of my favourite jokes in Sopio) A pair of bear arms to go over your regular ones. Get it? Bear arms? BEAR arms?

I personally would love for Greek god/goddess cards, or gods and goddesses from other pantheons, to make their way in, but I agree they could be too powerful or too easy to overpower if you know their myths. Plus it would be hard to choose which ones to include, as you obviously couldn't include them all (although what a great second expansion that could be! I'd buy that in a heartbeat!)
What about a generic "Goddess" card, just a stereotypical Greek goddess look, but not any one goddess in particular and thus open to lots of interpretation? I think that could be really cool.

warriors:
Krampus (a creature from Alpine folklore who punishes bad children during the Yule season)
Jack the Ripper (A London serial killer from the late 1800s)
Basilisk (Legendary king of serpents that can cause death with a single glance)
battlefields:
Comic Book City (a city littered with criminals and cops)
Super Villain Hideout (a large facility full of traps)
Graveyard (full of zombies and ghosts)
Post Apocalyptic Wasteland (large dry irradiated landscape with mutants)
Prehistoric Jungle (man eating plants, giant bugs, and dinosaurs)
items:
Utility Belt (full of gadgets to help get out of tight spots)
Apple of Discord (Golden apple inscribed with the words "to the fairest" used by the goddess Eris)
Cupid's bow (used to cause infatuation in one of the combatants)

I just saw your comment on the Hankgames playthough. Would you consider reincorporating the genie into the expansion if it received support? I really like the car salesman/sleazy night club owner art and it seems like it could be really interesting to play, even with a separate wishing item.

Battlefields:
Bottomless Pit - constant falling, you actually do not need to fly
Underwater Castle - as seen in the little mermaid
Winter Landscape - a heavily snowed over area, typically a forest
A Doll House - including children trying to play with you
A Courtroom - everything you say will be used against you
Inside Of A Treasury - dual heist

Items:
Magical Portrait - the portrait is hurt instead of the warrior
Flute - they always do something magical
Four Clover - handpicked by a little girl
Scout's Backpack - everything you need to survive contained within
Blow Darts - these can kill an elephant instantly
User Manual - rtfm!
Love Potion - a month worth of dating condensed in one bottle
Note From Future Self - not sure how I got this, so how do I know how to give it?

Warriors
- “Otherworldly AI Power” trundles around using some sort of intergalactic probe and exerts its vast knowledge and tech over civilizations it comes across. Can get into any connected system and solve practically any problem. [Inspiration “Fire Upon the Deep” by Vernor Vinge]
- “Emergent AI” present to some degree in practically anything that has had any sort of fleeting connection to the Internet. Has no central point of origin and can use most tech against any opponent. It could be scatterbrained and distractible though adept at sowing misinformation.
- “Affable though jaded veteran videogame coder” [could probably kick Medusa’s behind if able to determine enough of the problem parameters]

Battlefields
- “Derelict Spacecraft” The systems could be failing in various ways and combatants would have to be careful not to puncture hull or otherwise wreck vital systems needed to live or potentially to leave area if successful.
- “Game Developer Conference” All the crazy stuff that exhibitors have to wow people in their booths plus the exhibitors and the attendees could flock to a combatants banner based on the draw to their particular geek compass. [Other conventions have been suggested and thought this could be fun.]

Items
HUD/Cortex Shunt with direct link to all-knowing AI power - essentially an instant recall super Wikipedia.
Nanotech assemblers - build or reassemble just about anything if correct/sufficient materials and time are at hand. Could create other items or even alter/repair/hamper/attack warriors.

@Doug Martin Story War already has cartoon physics!
@Lloyd Pyes we totally wanna do a Monkey King card!
@Essay Butler oh cool! Maybe like a Davey Jones card? We have a Final Destination Battlefield, called "Plains"
@Gary Owen haha a lot of people have suggested a convention center, hmm.

I had an idea for two Battlefields: Ancient indian burial ground and DOUBLE ancient indian burial ground! "Hey, did you know...This ancient indian burial ground is built on...AN ANCIENT INDIAN BURIAL GROUND!"
and an anime/comic con. The smell. The costumes. The dealers room....X_x

For a Warrior card, I'd like to suggest The Monkey King, also commonly referred to as Sun Wukong or Son Goku. Now in my opinion, there's two ways you could go with this if you chose this suggestion:
1. Make him a slouchy burnout sort of character who uses the staff he's associated with as like a bar or something for him to lean on
or
2. Turn him into a bulky yet agile luchador with a monkey king motif.

I saw someone suggest a 2D world as a Battlefield. Let me take that a step further and say a cartoon world where cartoon physics apply. So you could paint a tunnel on a wall and trick your opponent to go through it, or take an anvil from above and walk away like a slinky. I guess no one would die with such physics so it would be up to the judge to decide when someone has won, but I think it could work. I mean, the coyote never dies, but he also never succeeds; the episode just ends with him losing. So, it would be up to the judge to decide when the "episode" (i.e. round) ended and who took the most hits.

Elifino - An Elephant and a Rhino do the fusion dance and make this monstronsity. Maybe it has huge dumbo ears, the silly blue hat and a giant horn for goring. That is if he doesnt trip over his ears. Good thing he can fly.

Honey Badger Man - Bad ass animal, nut job vigilante.... Nuff said.

Weapons:

Magic Beans - The musical fruit the more you eat the more a beanstalk shoots right outta your ass. Ouch!

My first thought for a warrior is an extremely intelligent, telepathic Brain in a Jar. It wouldn't need to use actual mind control(though that could work), it would just be so smart that it could kill you by convincing you to do something that gets you killed, or by talking to others and getting them to fight for it. It could also be Telekinetic, but I'm guessing you already have a proper Psychic so that might be redundant.

For an item, I recommend "Prep Time", so more Batman-ish warriors could be allowed to set traps and such.

And to round it out, I think an M.C. Escher painting would work fantastically for a Battlefield.

I would love to see yokai incorporated into this game, if they haven't been already! Yokai are traditional Japanese monsters from old folk tales, such as Kitsune, Kappa, Tengu, Oni, and much, much more. In fact Tsukumogami, a type of yokai that are ordinary household items come to life on their 100th birthday, could also be items. Probably the best known of the Tsukumogami (due to its appearance in older Nintendo games,) is the Kasa-obake, an umbrella with a single eye and a ridiculous tongue that hops around on one foot. Going with the Japanese theme here, some potential battlefields could be a Palace Garden, a Shinto shrine, or a graveyard filled with fallen warriors. All of those suggestions are based off real places in Japan (cough cough the Imperial Gardens, Meji Shrine, Grave of the 47 Ronin.) Or you could do a less specific place such as a rice paddy.

Greek Gods would be too easy to over-power. I’d suggest sticking with the monsters: The Hydra, Sphynx, Charybdis and Scylla. You could include a Nemaen Lion, or you could just make a more general “King Lion” (reversed for copyright reasons) so people can play it from multiple different perspectives.

From other cultures you could include La Llorona (is there a good ghost card already?), King Arthur, Annie Oakley (I loved Aramis suggestion), a Terracotta Soldier, or a Kelpie. For Norse mythology you could include a Frost Giant or Grendel.

As far as battlefields go, I’d just like one where everything is underwater. I’d be fun to explain/make up how certain warriors can survive there, and it flips certain advantages like flight.

Mad Scientist? Someone suggested their lair, but they could be a decent warrior as well. Could fit well with the Jekyll/Hyde idea.
I was also thinking hippocamp/sea-horse, but I don't really know how'd you play it as a warrior. Might be better as an item? "The (Trusty) Steed"? Though that could be a warrior, I guess.
Also aside from a genie bottle there could also be a genie/jinn warrior, probably drawing a bit more on the desert/fire spirit aspect than just plain wish-giving.
Also (again adding to something below), apples in general seem to cause a lot of problems. Poison Apple, Forbidden Fruit (wasn't technically an apple but eh), Apple of Discord, etc. Not sure if they'd work better as their own items or just as an apple/fruit that you play however you want. Forbidden Fruit particularly could be cool as a way to lure characters into traps.

I wouldn't be surprised if something like this has been suggested, but having some form of monster-movie Kaiju as a Warrior would dovetail nicely with both the Sci-fi and Asian focuses of the expansion.